225k views
5 votes
Write a polynomial P(x) of degree 4 and with zeros 1, 3/2, (which of multiplicity one) and 0 (of multiplicity 2).

User Fxnn
by
8.9k points

1 Answer

4 votes

Answer

The polynomial is

P(x) = 2x⁴ - 5x³ + 3x²

Step-by-step explanation

We are told to write a polynomial of degree 4 with zeros (roots)

x = 1

x = (3/2) = 1.5

x = 0

x = 0 (multiplicity of 2 means it appears twice)

So, we can piece together the polynomial

P(x) = (x - 1) (x - 1.5) (x) (x)

We can write this as

P(x) = x² (x - 1) (x - 1.5)

= (x³ - x²) (x - 1.5)

We can multiply through by 2 to turn the 1.5 into a whole number

P(x) = (x³ - x²) (2x - 3)

= x³ (2x - 3) - x² (2x - 3)

= 2x⁴ - 3³ - 2³ + 3x²

= 2x⁴ - 5x³ + 3x²

Hope this Helps!!!

User Benjamin Smith Max
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.